Three-dimensional formation apparatus, three-dimensional formation method, and computer program

ABSTRACT

A three-dimensional formation apparatus includes a head-unit which can discharge liquid in a first-direction and a control-unit which controls the head-unit. The control-unit forms a hollow on a changed portion where an outline of a cross section object is simultaneously changed in a second-direction and a third-direction towards the inside from the outline of the cross section object in the second-direction or the third-direction, in a first cross section object formation process and executes a filling process of discharging the liquid containing a second quantity which is larger than a first quantity to the hollow so as to come in contact with the cross section object formed in the first cross section object formation process, to fill at least a part of the hollow with the liquid, after the first cross section object formation process is executed and before the second cross section object formation process is executed.

BACKGROUND

1. Technical Field

The present invention relates to a three-dimensional formationapparatus.

2. Related Art

In recent years, a three-dimensional formation apparatus using aprinting technology has been paid attention. For example, an ink jettechnology generally used in a printing technology is used inthree-dimensional formation apparatuses disclosed in JP-A-06-218712,JP-A-2005-67138, and JP-A-2010-58519. In the three-dimensional formationapparatuses using an ink jet technology, a three-dimensional object isformed by performing a step of discharging liquid having curingproperties and forming a cross section object for a layer along ahorizontal direction (XY direction), over a plurality of layers in aheight direction (Z direction).

In a predetermined formation resolution, the ink jet-typethree-dimensional formation apparatus discharges liquid to predeterminedcoordinates and forms dots to form a cross section object. Accordingly,an outline parallel to an X or Y direction can be smoothly formed, but adeviation of coordinates between adjacent dots is generated regarding anoutline inclined in the above directions, and jaggy is generated.Particularly, jaggy is easily noticed in a case where an angle inclinedin the X or Y direction is an acute angle.

In a printing technology of a two-dimensional image, it is possible toprevent generation of jaggy by forming small dots, for example, in aportion where the deviation of coordinates is generated. However, whensmall dots are formed in a portion where the deviation of coordinates isgenerated in a case of forming a three-dimensional object, a height ofthe portion is decreased, and it is difficult to form an appropriatethree-dimensional shape. Accordingly, it is difficult to simply applythe printing technology of a two-dimensional image to the formationprocess of a three-dimensional object. Thus, in the three-dimensionalformation apparatus which discharges liquid and forms athree-dimensional object, it is necessary to obtain a technology whichcan effectively prevent generation of jaggy in an object to be formed.

SUMMARY

The invention is realized in the following forms.

(1) According to an aspect of the invention, there is provided athree-dimensional formation apparatus which forms a three-dimensionalobject, the apparatus including: a head unit which discharges liquidwhich is one material of the object in a first direction, among thefirst direction, a second direction, and a third direction orthogonal toeach other; and a control unit which forms the object by laminating theplurality of cross section objects by executing a cross section objectformation process of forming a cross section object for one layer of theobject several times by discharging the liquid containing a quantityequal to or smaller than a first quantity to a designated coordinateamong coordinates representing a position in the second direction and aposition in the third direction, by controlling the head unit, in whichthe control unit forms a hollow on a changed portion where an outline ofthe cross section object is simultaneously changed in the seconddirection and the third direction towards the inside from the outline ofthe cross section object in the second direction or the third direction,in the first cross section object formation process among the crosssection object formation processes executed several times, and executesa filling process of discharging the liquid containing a second quantitywhich is larger than the first quantity to the hollow so as to come incontact with the cross section object formed in the first cross sectionobject formation process, to fill at least a part of the hollow with theliquid, after the first cross section object formation process isexecuted and before the second cross section object formation process isexecuted. In this case, since the hollow is formed in the portion wherethe outline of the cross section object is simultaneously changed in thesecond direction and the third direction, and then the hollow is filledby discharging the liquid containing the quantity (second quantity)which is larger than the normal quantity (first quantity) to the hollow,it is possible to effectively prevent generation of jaggy on the outlineinclined in the second direction or the third direction.

(2) The three-dimensional formation apparatus according to the aspect ofthe invention may further include a curing energy application unit whichapplies curing energy for curing the liquid, and the curing energyapplication unit may apply the curing energy to the discharged liquid,after the liquid is discharged in the first cross section objectformation process and before the filling process is executed at aninterval of a first time period, and may apply the curing energy to thedischarged liquid, after the liquid is discharged in the filling processand before the second cross section object formation process is executedat an interval of a second time period which is longer than the firsttime period. In this case, since the curing energy is applied at theinterval of the first time period after the liquid is discharged in thecross section object formation process, it is possible to preventdistortion of the shape of the hollow. Accordingly, in the subsequentfilling process, it is possible to accurately discharge the curableliquid to the hollow. In addition, since the curing energy is applied atthe interval of the second time period which is longer than the firsttime period, after filling the hollow with the liquid, it is possible tosufficiently apply time only for filling the hollow with the liquid.Therefore, it is possible to more effectively prevent the generation ofjaggy on the outline.

(3) In the three-dimensional formation apparatus according to the aspectof the invention, the coordinate to which the liquid is discharged inthe cross section object formation process may have the elementcorresponding to each coordinate and may be designated bytwo-dimensional raster data in which a gradation value corresponds toeach element, and the changed portion may be a portion including a firstelement in which the gradation value is less than 100% and a secondelement which comes in contact with the inside of the first element onthe second direction side or the third direction side, when a portioncorresponding to the outline of the cross section object of the rasterdata is subjected to a smoothing process. In this case, since the hollowis formed on the portion where the gradation value is less than 100%when the smoothing process of the raster data representing the crosssection object is performed, it is possible to form the hollow in aposition effective for preventing the generation of jaggy.

(4) In the three-dimensional formation apparatus according to the aspectof the invention, the second quantity may be a quantity corresponding toa value obtained by adding the gradation value of the first element andthe gradation value of the second element. In this case, since it ispossible to acquire the quantity of the liquid to be discharged to thehollow according to the gradation value of the element present in theportion in which the hollow is formed, it is possible to accuratelyacquire the quantity of the liquid for filling the hollow.

(5) In the three-dimensional formation apparatus according to the aspectof the invention, the shape of the object may be represented withpolygon data which is an assembly of a plurality of polygons, and thefirst element may be an element corresponding to a position where thepolygon crosses. In this case, since the first element in which thegradation value is less than 100% in the smoothing process is determinedbased on whether or not the polygon representing the three-dimensionalobject crosses the element, it is possible to accurately specify thefirst element.

(6) In the three-dimensional formation apparatus according to the aspectof the invention, the gradation value of the first element may be avalue corresponding to a ratio of a volume remaining when a volume iscut by the polygon, to the volume of the first element occupying athree-dimensional space. In this case, it is possible to accuratelycalculate the gradation value of the first element in which thegradation value is less than 100% in the smoothing process.

(7) In the three-dimensional formation apparatus according to the aspectof the invention, the second element may be an element adjacent to adirection of a large component among a component in the second directionand a component in the third direction of an inward normal line of thepolygon which crosses the first element, among an element in the seconddirection adjacent to the first element and an element in the thirddirection adjacent to the first element. In this case, it is possible toaccurately specify the formation direction of the hollow which canprevent the generation of jaggy.

The invention can be realized in various forms, in addition to theaspects of the three-dimensional formation apparatus. For example,invention can be realized in forms of a three-dimensional formationmethod of forming a three-dimensional object by a three-dimensionalformation apparatus, a computer program causing a computer to control athree-dimensional formation apparatus and form a three-dimensionalobject, and a non-primary recording medium in which the computer programis recorded.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described with reference to the accompanyingdrawings, wherein like numbers reference like elements.

FIG. 1 is an explanatory diagram showing a schematic configuration of athree-dimensional formation apparatus.

FIG. 2 is a flowchart of a three-dimensional formation process.

FIG. 3 is a flowchart showing details of a smoothing process.

FIG. 4 is an explanatory diagram showing a positional relationshipbetween a target element and a polygon.

FIGS. 5A to 5D are explanatory diagrams showing a method of forming maindata and auxiliary data.

FIG. 6 is a diagram showing a concept of a second element.

FIGS. 7A to 7C are explanatory diagrams showing a state where a crosssection object is formed by a head unit.

FIG. 8 is an explanatory diagram showing a specific controlling methodof curing energy application units.

FIGS. 9A and 9B are explanatory diagrams showing a state where anoutline portion of the cross section object is formed by curable liquidand a support material.

FIG. 10 is a flowchart showing a smoothing process of a thirdembodiment.

FIG. 11 is a flowchart showing a smoothing process of a fourthembodiment.

FIG. 12 is an explanatory diagram showing a schematic configuration of athree-dimensional formation apparatus of a fifth embodiment.

DESCRIPTION OF EXEMPLARY EMBODIMENTS A. First Embodiment

FIG. 1 is an explanatory diagram showing a schematic configuration of athree-dimensional formation apparatus as a first embodiment. Athree-dimensional formation apparatus 100 includes a formation unit 10,a powder supply unit 20, a flattening mechanism 30, a powder collectionunit 40, a head unit 50, curing energy application units 60, and acontrol unit 70. A computer 200 is connected to the control unit 70. Thethree-dimensional formation apparatus 100 and the computer 200 can becollectively treated as a three-dimensional formation apparatus in abroad sense. FIG. 1 shows an X direction, a Y direction, and a Zdirection orthogonal to each other. The Z direction is a direction alonga vertical direction and the X direction is a direction along ahorizontal direction. The Y direction is a direction vertical to the Zdirection and the X direction. The Z direction corresponds to a firstdirection, the X direction corresponds to a second direction, and the Ydirection corresponds to a third direction.

The formation unit 10 is a tank-shaped structure in which athree-dimensional object is formed. The formation unit 10 includes aformation stage 11 which is flat in the XY direction, a frame body 12which surrounds around the formation stage 11 and stands in the Zdirection, and an actuator 13 which moves the formation stage 11 alongthe Z direction. The formation stage 11 moves in the Z direction in theframe body 12 by the control unit 70 controlling an operation of theactuator 13.

The powder supply unit 20 is an apparatus which supplies powder into theformation unit 10. The powder supply unit 20 is, for example, configuredwith a hopper or a dispenser.

The flattening mechanism 30 is a mechanism for flattening powdersupplied into the formation unit 10 or onto the frame body 12 by movingan upper surface of the formation unit 10 in the horizontal direction(XY direction), and forming a powder layer on the formation stage 11.The flattening mechanism 30 is, for example, configured with a squeegeeor a roller. The powder extruded from the formation unit 10 by theflattening mechanism 30 is discharged into the powder collection unit 40provided adjacent to the formation unit 10.

The three-dimensional formation apparatus 100 of the first embodimentuses liquid having curing properties (hereinafter, referred to ascurable liquid) and the powder as the materials of the three-dimensionalobject. As the curable liquid, a mixture of a resin material of liquidhaving a monomer and an oligomer bound with the monomer as maincomponents, and a polymerization initiator which turns into anexcitation state and starts polymerization by promoting the monomer andthe oligomer, when an ultraviolet light beam is emitted, is used. Forthe monomer in the curable liquid, a monomer having comparatively lowmolecular weight is selected so that a viscosity of the curable liquidis set as a low viscosity to be discharged dropwise from the head unit50, and the number of monomers contained in one oligomer is alsoapproximately adjusted to several molecules. The curable liquid hasproperties to be rapidly cured to be solid by polymerizing the monomerswith each other to grow the monomers to the oligomer or polymerizingsome oligomers with each other, when the curable liquid is irradiatedwith the ultraviolet light beam and the polymerization initiator turnsinto an excitation state. In the embodiment, powder in which apolymerization initiator which is different from the polymerizationinitiator contained in the curable liquid is attached to the surfacethereof is used as the powder. The polymerization initiator attached tothe surface of the powder has properties of starting polymerization ofthe monomers or the oligomer by promoting it, when the polymerizationinitiator comes in contact with the curable liquid. Accordingly, whenthe curable liquid is supplied to the powder in the formation unit 10,the curable liquid permeates the inside of the powder and comes incontact with the polymerization initiator on the surface of the powderto be cured. As a result, in a portion to which the curable liquid isdischarged, the powders are bound by the cured curable liquid. When thepowder having the polymerization initiator attached to the surfacethereof is used as the powder, it is also possible to use curable liquidnot containing the polymerization initiator.

The head unit 50 is an apparatus which receives the supply of thecurable liquid from a tank 51 connected to the head unit 50 anddischarges the curable liquid to a powder layer in the formation unit 10along the Z direction. The head unit 50 can be moved in the X directionand the Y direction with respect to the three-dimensional object formedin the formation unit 10. The head unit 50 can be moved in the Zdirection relatively to the three-dimensional object by the formationstage 11 in the formation unit 10 which moves in the Z direction. Thehead unit 50 of the embodiment is a so-called piezoelectric driving typeliquid droplet discharge head. By filling a pressure chamber providedwith fine nozzle holes with the curable liquid and bending a side wallof the pressure chamber using a piezoelectric element, the piezoelectricdriving type liquid droplet discharge head can discharge a volume of thecurable liquid corresponding to a decreased amount of a volume of thepressure chamber as liquid droplets. Since the control unit 70 whichwill be described later controls a voltage waveform applied to thepiezoelectric element, it is possible to adjust quantity of the curableliquid per droplet discharged from the head unit 50 in a stepwisemanner. Nozzle holes through which the curable liquid is discharged, arearranged on the head unit 50 along the Y direction.

The curing energy application units 60 are apparatuses which applyenergy for curing the curable liquid discharged from the head unit 50.In the embodiment, the curing energy application units 60 are configuredwith a final curing light emitting apparatus 61 and a temporary curinglight emitting apparatus 62 which are disposed so as to interpose thehead unit 50 in the X direction. When the head unit 50 is moved, thecuring energy application units 60 are also moved according to themovement thereof. The ultraviolet light beam is emitted from the finalcuring light emitting apparatus 61 and the temporary curing lightemitting apparatus 62 as curing energy for curing the curing liquid. Thetemporary curing light emitting apparatus 62 is used in performingtemporary curing for fixing the discharged curable liquid to a landedposition thereof. The final curing light emitting apparatus 61 is usedfor completely curing the curable liquid after the temporary curing. Theenergy of the ultraviolet light beam emitted from the temporary curinglight emitting apparatus 62 is energy of 20% to 30% of the ultravioletlight beam emitted from the final curing light emitting apparatus 61,for example. The temporary curing is also referred to as “pinning” andthe final curing is also referred to as “curing”.

The control unit 70 is an apparatus which controls the actuator 13, thepowder supply unit 20, the flattening mechanism 30, the head unit 50,and the curing energy application units 60 and forms thethree-dimensional object. The control unit 70 includes a CPU and amemory. The CPU realizes a cross section object formation function and afilling function by loading computer programs stored in a memory or arecording medium in the memory and executing the programs. The crosssection object formation function is a function of controlling the headunit 50 and forming a cross section object for one layer of thethree-dimensional object by discharging each of the curable liquidcontaining a first quantity to a designated coordinate among thecoordinates in the X direction and the Y direction. In the cross sectionobject formation function, a hollow is formed on a changed portion wherethe outline of the cross section object is simultaneously changed in theX direction and the Y direction towards the inside from the outline ofthe cross section object in the second direction or the third direction.The filling function is a function of discharging the curable liquidcontaining a second quantity which is smaller than the first quantity tothe hollow of the cross section object formed by the cross sectionobject formation function and filling at least a part of the hollow withthe curable liquid. The specific process content for realizing thesefunctions will be described later. These functions of the control unit70 may also be applied to the computer 200 side.

A procedure of forming the three-dimensional object by thethree-dimensional formation apparatus 100 will be simply described.First, the computer 200 slices three-dimensional data representing ashape of a three-dimensional object according to a formation in the Zdirection (for example, 600 dpi) and generates a plurality of crosssection data items along the XY direction. The cross section data itemshas a predetermined formation resolution (for example, 600 dpi×600 dpi)are represented as two-dimensional raster data in which a gradationvalue is stored with respect to each element. The gradation value storedwith respect to each element represents the quantity of the curableliquid discharged to the XY coordinate corresponding to the element.That is, in the embodiment, the coordinate to which the curable liquidand the quantity of the curable liquid to be discharged are designatedfor the control unit 70 of the three-dimensional formation apparatus 100by the raster data. For example, when the gradation value is designatedas 100% with respect to a certain coordinate, a quantity of the curableliquid which can fill 100% of a volume of an element (voxel) in athree-dimensional space corresponding to the coordinate, is dischargedfrom the head unit 50. Herein, the quantity of the curable liquid perdroplet discharged from the head unit 50 is limited to the finite kindsof quantity. Accordingly, when the gradation value is designated by theraster data, the control unit 70 makes the quantity of the curableliquid corresponding to the designated gradation value to the closestquantity among the predetermined kinds of quantity. For example, whenthe quantities of the curable liquid which can be discharged from thehead unit 50 are nine types of 0%, 25%, 50%, 75%, 100%, 125%, 150%,175%, and 200%, the control unit 70 selects the quantity closest to thedesignated gradation value among the nine types of quantity of thecurable liquid. When the gradation value is designated, the control unit70 may multiply a predetermined coefficient by the designated gradationvalue according to a curing shrinkage ratio of the curable liquid, forexample.

When the cross section data is acquired from the computer 200, thecontrol unit 70 of the three-dimensional formation apparatus 100controls the powder supply unit 20 and the flattening mechanism 30 andforms the powder layer in the formation unit 10. The control unit drivesthe head unit 50 and discharges the curable liquid to the powder layeraccording to the cross section data, and then controls the curing energyapplication units 60 and emits the ultraviolet light beam towards thedischarged curable liquid. By doing so, the curable liquid is cured andpowders are bound with each other by the ultraviolet light beam, and thecross section object corresponding to the cross section data for onelayer is formed in the formation unit 10. When the cross section objectfor one layer is formed as described above, the control unit 70 drivesthe actuator 13 and moves the formation stage 11 downwards in the Zdirection by an amount of a lamination pitch corresponding to theformation resolution in the Z direction. When the formation stage 11 ismoved downwards, the control unit 70 forms a new powder layer on thecross section object which is previously formed on the formation stage11. When the new powder layer is formed, the control unit 70 receives anext cross section data item from the computer 200, discharges thecurable liquid to a new powder layer, and irradiates the new powderlayer with the ultraviolet light beam, to form a new cross sectionobject. As described above, when the cross section data of each layer isreceived from the computer 200, the control unit 70 forms the crosssection object for each layer and forms the three-dimensional object bylaminating the layer, by controlling the actuator 13 or the powdersupply unit 20, the flattening mechanism 30, the head unit 50, and thecuring energy application units 60.

Next, the more specific process content of the three-dimensionalformation process of the embodiment will be described.

FIG. 2 is a flowchart of the three-dimensional formation processexecuted by the computer 200 and the three-dimensional formationapparatus 100. In the embodiment, first, the computer 200 acquires thethree-dimensional data representing the shape of the three-dimensionalobject from a recording medium or a network, or an application programexecuted in the computer 200 (Step S100). The three-dimensional data,for example, is represented as three-dimensional polygon data,two-dimensional raster data for each cross section, and two-dimensionalvector data for each cross section. In the embodiment, thethree-dimensional data is represented as the polygon data. When thethree-dimensional data is acquired, the computer 200 performs thesmoothing process (Step S200).

FIG. 3 is a flowchart showing details of the smoothing process. In thesmoothing process, the raster data for each cross section is generatedfrom the three-dimensional data. First, the computer 200 cuts out onecross section having a thickness according to the formation resolutionin the Z direction from the three-dimensional polygon data (Step S202).When one cross section is cut out, the computer 200 specifies theelement (coordinate) on the raster data for determining the gradationvalue in the following process (Step S204). Hereinafter, this element isreferred to as a “target element”.

When the target element is specified, the computer 200 determineswhether or not there is a target element on the outside of the polygon(Step S206). When it is determined that there is a target element on theoutside of the polygon (Step S206: YES), the computer 200 determines thegradation value of the target element as 0% (Step S208). When it isdetermined that there is not a target element on the outside of thepolygon (Step S206: NO), the computer 200 further determines whether ornot the polygon crosses the target element (Step S210).

FIG. 4 is an explanatory diagram showing a positional relationshipbetween the target element and the polygon. FIG. 4 shows a state where apolygon PL crosses a cubic lattice VX corresponding to the targetelement. In Step S210 described above, when it is determined that thepolygon crosses the target element as shown in FIG. 4 (Step S210: YES),the computer 200 calculates the gradation value of the target elementbased on the following equation (1) (Step S212).Gradation value=maximum gradation value(100%)×polygon volume ratio  (1)

Herein, the polygon volume ratio is a ratio of a remaining volume VL ina case where a volume of the cubic lattice VX corresponding to thetarget element is cut out by the polygon, with respect to the volumethereof.

In Step S210 described above, when it is determined that the polygondoes not cross the target element (Step S210: NO), the surfacerepresented as the polygon and the surface on the outside of the cubiclattice represented as the target element coincide with each other, andaccordingly, the computer 200 determines the gradation value of thetarget element as 100% (Step S214).

When the gradation value of the target element is determined by theprocesses described above, the computer 200 determines whether or notthe determination of the gradation value is completed regarding theentire element in the current cross section (Step S216). When it isdetermined that the gradation value regarding the entire element in thecurrent cross section is not determined (Step S216: NO), the processreturns to Step S204 and the computer 200 determines the gradation valueregarding the other element.

When it is determined that the gradation value regarding the entireelement in the current cross section is determined (Step S216: YES), thecomputer 200 determines whether or not the determination of thegradation value regarding the entire cross section is completed (StepS218). When it is determined that the gradation value regarding theentire cross section is not completed (Step S218: NO), the processreturns to Step S202 and the computer 200 cuts out the next crosssection and determines the gradation value regarding the entire elementin the cross section. When it is determined that the gradation valueregarding the entire element is completed (Step S218: YES), the computer200 accommodates raster data in which the gradation value regarding thedetermined entire element is accommodated, in a memory or a recordingmedium, regarding the entire cross section as the cross section data(Step S220), and the smoothing process is completed.

The description returns to FIG. 2. When the smoothing process describedabove is completed, the computer 200 generates the main data and theauxiliary data based on the raster data accommodated in a memory by thesmoothing process (Step S300). The main data is data which is mainlyused when the three-dimensional formation apparatus 100 forms the crosssection object. The auxiliary data is data for refilling the curableliquid to a part of the cross section object formed using the main data.

FIGS. 5A to 5D are explanatory diagrams showing a method of generatingthe main data and the auxiliary data regarding one cross section by thecomputer 200. FIG. 5A is a reference diagram showing an outline portionof the raster data when the smoothing process described above isperformed. When the smoothing process described above is not performed,the gradation value of the raster data is represented as any one of 0%or 100%, and accordingly jaggy having a shape of a difference in levelas shown in FIG. 5A is generated on the outline portion represented asthe raster data. Particularly, jaggy is easily noticed in a case wherean angle inclined in each of the X and Y directions is an acute angle.Meanwhile, when the smoothing process described above is not performed,the gradation value of the difference-in-level portion is represented asa half tone and the outline is smoothly represented, as shown in FIG.5B. FIGS. 5A to 5D show an example where the gradation values arerepresented as five types of 0%, 25%, 50%, 75%, and 100%.

As shown in FIG. 5C, the computer 200 performs the thinning of firstelements EL1 in which the gradation value is less than 100%, and secondelements EL2 which are adjacent to the first elements EL1 on the Xdirection side and the inside of the Y direction side, from the smoothedraster data represented as shown in FIG. 5B, and accordingly, generatesthe main data. In the example shown in FIGS. 5A to 5D, all of thegradation values of the second elements EL2 are 100%. When the thinningof the first elements EL1 and the second elements EL2 is performed,hollows D is formed in the X direction and the Y direction, on thechanged portion where the outline of the cross section object issimultaneously changed in the X direction and the Y direction, in theshape represented as the main data. FIGS. 5A to 5D show an example inwhich the hollows are formed in the Y direction. As described below, thecomputer 200 determines to set which element adjacent to the X directionside or the Y direction side with respect to the first element EL1 asthe second element EL2, that is, to select a direction in which thehollow is formed from the first element EL1.

FIG. 6 is a diagram showing a concept of a specifying method of thesecond element EL2. First, the computer 200 acquires an inward normalline AL of the polygon PL which crosses the first element EL1. An Xcomponent ALX and a Y component ALY of the normal line thereof areacquired, and the element adjacent to the direction of the componenthaving a large value among the components (Y component ALY in a case ofFIG. 6) is specified as the second element EL2. When the position of thesecond element EL2 is specified as described above, it is possible toappropriately determine the direction in which the hollow is formed,with respect to the inclined outline.

When the main data in which the hollow D is formed, is generated asdescribed above, the computer 200 generates the auxiliary data.Specifically, as shown in FIG. 5D, the auxiliary data is generated byadding the gradation value of the first element removed when generatingthe main data and the gradation value of the second element adjacent tothe first element. The computer 200 generates the main data and theauxiliary data regarding each cross section by executing the processdescribed above regarding the entire cross sections. When the main dataand the auxiliary data are generated, the computer 200 accommodates thedata items in a memory or a recording medium regarding the entire crosssections as the cross section data items.

After the main data and the auxiliary data are generated regarding theentire cross sections by the computer 200, the control unit 70 of thethree-dimensional formation apparatus 100 acquires the cross sectiondata items (the main data and the auxiliary data) representing the crosssection of the lowest layer from the computer 200 (Step S400 of FIG. 2).When the cross section data is acquired, the control unit 70 executes across section object formation process using the main data among thecross section data items thereof (Step S500). The cross section objectformation process is a process of discharging the curable liquidcontaining the first quantity to each coordinate in the X direction andthe Y direction while moving the head unit 50 in the X direction and theY direction, to form the cross section object which is a part of thethree-dimensional object. The first quantity in the embodiment is aquantity corresponding to the 100% of the gradation value and is aquantity of the curable liquid necessary for filling the volume of theelement (voxel) corresponding to one coordinate. In the embodiment, allof the dots to be formed by the main data are formed with the curableliquid containing the first quantity, but the dots may be formed bydistinguishing the curable liquid containing the first quantity and thecurable liquid having less than the first quantity. In the embodiment,the head unit 50 is moved in the Y direction for each time when thedischarge of the curable liquid in the X direction is completed, and thecross section object is formed over the entire XY plane.

FIGS. 7A to 7C are explanatory diagrams showing a state where the crosssection object is formed by the head unit 50. According to the crosssection object formation process performed in Step S500, the crosssection object is formed based on the main data shown in FIG. 5C.Accordingly, as shown in FIG. 7A, the hollow D is formed on the changedportion where the outline of the cross section object is simultaneouslychanged in the X direction and the Y direction towards the inside fromthe outline of the cross section object in the X direction or the Ydirection. As shown in FIG. 7A, in the embodiment, the hollow D isformed on the corner of the inside of the difference-in-level portion ofthe outline. In FIGS. 7A to 7C, for easy understanding, each dot isshown as the lattice, but all of the dots adjacent to each other arecontinuously connected to each other, in practice.

When the cross section object is formed based on the main data, thecontrol unit 70 controls the curing energy application units 60 andperforms the temporary curing of the discharged curable liquid (StepS600 of FIG. 2). By performing the temporary curing, it is possible tofix the shape of the hollow D. Herein, a time period from the timingwhen the curable liquid is discharged from the head unit 50 to thetiming when the curing energy for the temporary curing is applied to thecurable liquid, is referred to as a “first time period t1”.

After performing the temporary curing in Step S600 described above, thecontrol unit 70 continuously performs a filing process using theauxiliary data (Step S700). As shown in FIG. 7B, the filling process isa process of discharging the curable liquid containing the secondquantity corresponding to the gradation value represented as theauxiliary data to the hollow D of the cross section object, so as tocome in contact with the cross section object formed by the crosssection object formation process, to fill at least a part of the hollowD with the curable liquid. As described above, the auxiliary data isgenerated by adding the gradation value of the first element and thegradation value of the second element. In the embodiment, the gradationvalue of the second element is 100% and the gradation value of the firstelement is larger than 0% and smaller than 100%. Accordingly, the secondquantity represented as the auxiliary data is larger than the firstquantity (100%). For convenience of illustration, FIG. 7B shows thecurable liquid containing the second quantity to be ejected to the crosssection object in the positive Y direction, but the curable liquid isejected so as to come in contact with the inner wall of the hollow D inthe positive Z direction in practice.

As described above, when the filling process using the auxiliary data isperformed, the control unit 70 does not perform the temporary curing,but controls curing energy application units 60 and performs the finalcuring for the cross section object, at an interval of a second timeperiod t2 which is longer than the first time period t1 (Step S800 ofFIG. 2). By performing the processes from Step S400 to Step S800described above, the cross section object is formed for one layer.

FIG. 7C shows a state where the cross section is formed for one layer.In step s800 described above, the temporary curing is not performed tothe curable liquid discharged into the hollow D in the filing process.Accordingly, the curable liquid containing the second quantitydischarged into the hollow D is not immediately cured, approaches theentire hollow D by surface tension and a capillary phenomenon, andsmoothly fills the difference in level generated on the outline of thecross section object. By performing the final curing after the secondtime period t2 longer than the first period time t1 described above iselapsed, the cross section object formed by the main data and thecurable liquid formed by the auxiliary data are completely cured, andone cross section object is completed.

As described above, when the cross section object for one layer isformed, the control unit 70 determines whether or not the entire crosssection object is formed (Step S900 of FIG. 2). When it is determinedthat the entire cross section object is not formed (Step S900: NO), theprocess returns to Step S400 and the control unit 70 reads the nextcross section data and forms the cross section object for the nextlayer. Before forming the cross section object for the next layer, thecontrol unit 70 moves the formation stage 11 downwards and forms thepowder layer. In Step S900 described above, when it is determined thatthe entire cross section object is formed (Step S900: YES), the controlunit 70 finishes the three-dimensional formation process. Thethree-dimensional object is formed in the formation unit 10 byperforming a series of the three-dimensional formation process describedabove.

FIG. 8 is an explanatory diagram showing a specific controlling methodof the curing energy application units 60 in the three-dimensionalformation process described above. Hereinafter, the formation of thedots on the formation stage 11 while moving the head unit 50 from an endto the other end in the X direction is referred to as “scanning”. Atable shown in FIG. 8 shows that the cross section object formationprocess is performed by the main data when the head unit 50 performs thescanning in the positive X direction and then the filing process isperformed by the auxiliary data when the head unit 50 performs thescanning in the negative X direction. For convenience of description, inFIG. 8, the movement of the head unit 50 in the Y direction is omitted.

When forming the cross section object for the first layer, the finalcuring light emitting apparatus 61 is turned off and the temporarycuring light emitting apparatus 62 are turned on in the scanning inwhich the cross section object formation process is performed based onthe main data. Accordingly, after the curable liquid is discharged fromthe head unit 50 and landed on the powder layer, the head unit 50 movesin the positive X direction and the temporary curing is performed at thetiming when the temporary curing light emitting apparatus 62 arrives theupper portion of the curable liquid. The temporary curing can also beperformed after the curable liquid is discharged from the head unit 50and before the curable liquid is landed on the powder layer.

When the cross section object formation process based on the main datais completed, a scanning direction of the head unit 50 changes to thenegative X direction and the filling process based on the auxiliary datais performed. When the filling process is performed, the temporarycuring light emitting apparatus 62 is turned off and the final curinglight emitting apparatus 61 is also turned off. Accordingly, asdescribed above, after the auxiliary data is generated, the temporarycuring is not performed.

Next, when forming the cross section object for the second layer, bothof the final curing light emitting apparatus 61 and the temporary curinglight emitting apparatus 62 are turned on in the scanning in which thecross section object formation process is performed based on the maindata. Accordingly, first, the final curing is performed for the crosssection object for the first layer formed by the previous cross sectionobject formation process and the filling process by the final curinglight emitting apparatus 61, while the head unit 50 performs thescanning in the positive X direction, and then the curable liquid forforming the cross section object for the second layer is immediatelydischarged onto the cross section object for the first layer subjectedto the final curing, based on the main data. By doing so, the head unit50 moves in the positive X direction and the curable liquid istemporarily cured at the timing when the temporary curing light emittingapparatus 62 arrives to the upper portion of the curable liquid. Thatis, for the second layer, the final curing of the cross section objectfor the first layer, the formation of the cross section object for thesecond layer, and the temporary curing of the cross section object forthe second layer are performed in parallel in the first scanning. Then,the same control operation as that for the second layer is performed forthe curing energy application units 60, and the cross section objectsare successively subjected to the temporary curing and the final curing,and laminated with each other.

According to the control method of the curing energy application units60 shown in FIG. 8, since both the temporary curing and the final curingare not performed immediately after the filling process based on theauxiliary data is performed, it is possible to reliably set the secondtime period t2 which is after the curable liquid is discharged in thefilling process based on the auxiliary data and until the final curingis performed, to be longer than the first time period t1 which is afterthe curable liquid is discharged in the cross section object formationprocess based on the main data and until the temporary curing isperformed.

According to the three-dimensional formation apparatus 100 describedabove, the hollow is formed in the portion where the outline of thecross section object is simultaneously changed in the X direction andthe Y direction, and then the hollow is filled with the curable liquidto fill the hollow, and accordingly it is possible to effectivelyprevent generation of jaggy on the outline inclined in the X directionor the Y direction.

In the embodiment, since the temporary curing is performed after thecross section object having the hollow is formed, it is possible toprevent distortion of the shape of the hollow. Accordingly, in thesubsequent filling process, it is possible to accurately discharge thecurable liquid to the hollow. In addition, after filling the hollow withthe curable liquid, the temporary curing is not performed, and thus, itis possible to sufficiently apply time only for filling the hollow withthe curable liquid. Therefore, it is possible to more effectivelyprevent the generation of jaggy on the outline.

In the embodiment, the hollow is formed on the portion where thegradation value is less than 100% when the smoothing process of theraster data representing the cross section object is performed, andaccordingly, it is possible to form the hollow in a position effectivefor preventing the generation of jaggy.

In the embodiment, the quantity of the curable liquid to be dischargedto the hollow is calculated based on the gradation value of the elementpresent in the hollow, before forming the hollow with respect to theraster data, and accordingly, it is possible to accurately acquire thequantity of the curable liquid for filling the hollow.

In the embodiment, since the first element in which the gradation valueis less than 100% in the smoothing process is determined based onwhether or not the polygon representing the three-dimensional objectcrosses the element, it is possible to accurately specify the firstelement.

In the embodiment, since the gradation value of the element in which thegradation value is less than 100% in the smoothing process is calculatedaccording to a volume fraction of the polygon of the element, it ispossible to accurately calculate the gradation value.

In the embodiment, since the direction in which the hollow is formed onthe outline of the cross section object is specified according to thesize of the X component and the Y component of the normal line of thepolygon, it is possible to accurately specify the formation direction ofthe hollow which can prevent the generation of jaggy.

B. Second Embodiment

The three-dimensional formation apparatus 100 of the first embodimentforms the three-dimensional object using the curable liquid and thepowder. According to this, the three-dimensional formation apparatus 100of a second embodiment forms the three-dimensional object using asupport material, in addition to the curable liquid. The supportmaterial of the embodiment is liquid which is cured by curing energyequivalent to the curing energy for curing the curable liquid, and is amaterial which can be dissolved by putting into water or a predeterminedsolution after the curing and can be easily removed. When the supportmaterial is discharged to the outside of the outline of thethree-dimensional object, it is possible to prevent the spread of theoutline of the three-dimensional object formed with the curable liquidto the outside. In the three-dimensional formation apparatus 100 of thesecond embodiment, nozzles for discharging the curable liquid and thesupport material are respectively included in the head unit 50, and atank accommodating the curable liquid and a tank accommodating thesupport material are connected to the head unit 50. In the embodiment,the head unit 50 discharges the support material in the same scanning asthe scanning for discharging the curable liquid. The head unit 50 canalso discharge the support material in the scanning which is differentfrom the scanning for discharging the curable liquid.

FIGS. 9A and 9B are explanatory diagrams showing a state where theoutline portion of the cross section object is formed by curable liquidand a support material. In FIGS. 9A and 9B, the portion formed with thecurable liquid is represented as a black lattice and the portion formedwith the support material is represented as a white lattice. In theembodiment, the computer 200 also generates the main data and theauxiliary data for the portion to which the support material isdischarged (hereinafter, referred to as a support area) based on theraster data after the smoothing process, in the same manner as that ofthe portion to which the curable liquid is discharged (hereinafter,referred to as a normal area). The gradation value of each element ofthe raster data used for discharging the support material is a valueobtained by subtracting a value of the gradation value of each elementof the raster data used for discharging the curable liquid from 100%. Asshown in FIG. 9A, in the three-dimensional formation apparatus 100, whenthe cross section object formation process is executed based on the maindata, the hollow is formed on both of the normal area and the supportarea. When the filling process is executed based on the auxiliary dataafter executing the cross section object formation process, the curableliquid is discharged to the hollow of the normal area and the supportmaterial is discharged to the hollow of the support area. By doing so,as shown in FIG. 9B, the dot formed with the curable liquid and the dotformed with the support area are adjacent to each other in the hollowportion. As described above, when the dot formed with the curable liquidand the dot formed with the support area are adjacent to each other inthe hollow portion, it is possible to prevent the curable liquid fromflowing to the outside of the outline, due to the presence of thesupport material. Therefore, according to the second embodiment, it ispossible to more effectively prevent the generation of jaggy on theoutline of the three-dimensional object.

C. Third Embodiment

FIG. 10 is a flowchart showing a smoothing process of a thirdembodiment. In the first embodiment, the three-dimensional datarepresenting the shape of the three-dimensional object is represented asthe three-dimensional polygon data. Meanwhile, in the third embodiment,the three-dimensional data is represented as the raster data for eachcross section. The configurations of the three-dimensional formationapparatus 100 and the computer 200 of the third embodiment are the sameas those in the first embodiment.

In the smoothing process of the embodiment, first, the computer 200reads the three-dimensional data (Step S230). As described above, in theembodiment, the three-dimensional data is configured with the rasterdata for each cross section.

Then, the computer 200 compares a resolution in the XY direction of theread three-dimensional data (XY input resolution) and formationresolution in the XY direction of the three-dimensional formationapparatus 100 (XY formation resolution) to each other and determineswhether or not the XY input resolution is higher than the XY formationresolution (Step S232). When it is determined that the XY inputresolution is higher than the XY formation resolution (Step S232: YES),the computer 200 performs the general smoothing process for the rasterdata of all of the cross section and matches the resolution of theraster data of each cross section with the XY formation resolution (StepS234). Meanwhile, when it is determined that the XY input resolution islower than the XY formation resolution (Step S232: NO), the computer 200performs an interpolation process of a general image processingtechnology and the smoothing process for the raster data of all of thecross section and matches the resolution of the raster data of eachcross section with the XY formation resolution (Step S236).

Then, the computer 200 determines whether or not a pitch of thethree-dimensional data in the height direction (hereinafter, referred toas lamination pitch) matches with a formation resolution of thethree-dimensional formation apparatus 100 in the Z direction(hereinafter, referred to as Z resolution) (Step S238). When it isdetermined that the lamination pitch matches with the Z resolution (StepS238: YES), the computer 200 accommodates the data subjected to thesmoothing process so far in a memory or a recording medium (Step S240),and the process ends.

In Step S238 described above, when it is determined that the laminationpitch does not match with the Z resolution (Step S238: NO), the computer200 determines whether or not the lamination pitch is greater than the Zresolution (Step S242). When it is determined that the lamination pitchis greater than the Z resolution (Step S242: YES), the computer 200performs the interpolation between the cross sections according to thedifference of the pitch, and matches the lamination pitch and the Zresolution with each other by increasing the number of cross sections(Step S244). Meanwhile, when it is determined that the lamination pitchis smaller than the Z resolution (Step S242: NO), the computer 200performs thinning of the cross section data, reduces the number of thecross sections, and matches the lamination pitch and the Z resolution(Step S246). When the process in Step S244 or Step S246 is completed,the computer 200 accommodates the data subjected to the interpolation orthe thinning in a memory or a recording medium (Step S240), and theprocess ends.

According to the smoothing process of the third embodiment describedabove, it is possible to appropriately perform the smoothing process,even when the three-dimensional data is represented as the raster datafor each cross section.

In the third embodiment, there is no polygon used for specifying thesecond element at the time of generation of the main data. Accordingly,in the third embodiment, the second element is specified as follows.First, the computer 200 acquires a tangent line which circumscribes thefirst element in which the gradation value is less than 100%. The Xcomponent and the Y component of the normal line of the tangent line arecalculated, and an element adjacent to a direction facing the largercomponent among the components is specified as the second element, inthe same manner as in the method shown in FIG. 6. By doing so, it ispossible to appropriately specify the second element, also in the thirdembodiment.

D. Fourth Embodiment

FIG. 11 is a flowchart showing a smoothing process of a fourthembodiment. In the third embodiment, the three-dimensional data isrepresented as the raster data for each cross section. Meanwhile, in thefourth embodiment, the three-dimensional data is represented as vectordata for each cross section. The configurations of the three-dimensionalformation apparatus 100 and the computer 200 of the fourth embodimentare the same as those in the first embodiment.

In the smoothing process of the embodiment, first, the computer 200reads the three-dimensional data (Step S260). As described above, in theembodiment, the three-dimensional data is represented as the vector datafor each cross section.

Next, the computer 200 performs raster conversion of a general imageprocessing technology and the smoothing process for all of the crosssections of the read three-dimensional data (Step S262). The rasterconversion is a process of performing conversion from the vector datainto the raster data.

When the raster conversion and the smoothing process are performed, thecomputer 200 performs the interpolation of the cross section and thethinning of the cross section by executing the same processes as thosein Steps S238 and S242 to S246 of the third embodiment (Steps S264 andS268 to S272). The computer 200 accommodates the three-dimensional datasubjected to each process described above in a memory or a recordingmedium (Step S266), and the process ends.

According to the fourth embodiment described above, it is possible toappropriately perform the smoothing process, even when thethree-dimensional data is represented as the vector data for each crosssection.

Even in the fourth embodiment, there is no polygon used for specifyingthe second element at the time of generation of the main data, in thesame manner as in the third embodiment. Accordingly, in the fourthembodiment, the second element is specified as follows. First, thecomputer 200 acquires a vector which crosses the first element in whichthe gradation value is less than 100%. The X component and the Ycomponent of the normal line of the vector are calculated, and anelement adjacent to a direction facing the larger component among thecomponents is specified as the second element, in the same manner as inthe method shown in FIG. 6. By doing so, it is possible to appropriatelyspecify the second element, also in the fourth embodiment.

E. Fifth Embodiment

FIG. 12 is an explanatory diagram showing a schematic configuration of athree-dimensional formation apparatus of a fifth embodiment. Thethree-dimensional formation apparatus 100 of the first embodiment formsa three-dimensional object by discharging the curable liquid to thepowder supplied into the formation unit 10. Meanwhile, athree-dimensional formation apparatus 100 a of the fifth embodimentforms a three-dimensional object only with curable liquid containing aresin, without using the powder.

The three-dimensional formation apparatus 100 a includes the formationunit 10, the head unit 50, the curing energy application units 60, andthe control unit 70. In the same manner as in the first embodiment, theformation unit 10 includes the formation stage 11, the frame body 12,and the actuator 13. However, the frame body 12 may be omitted. A tank51 is connected to the head unit 50. The curing energy application units60 includes the final curing light emitting apparatus 61 and thetemporary curing light emitting apparatus 62. That is, mostconfigurations of the three-dimensional formation apparatus 100 a arecommon with the configurations of the three-dimensional formationapparatus 100 of the first embodiment, and has a configuration omittingthe powder supply unit 20, the flattening mechanism 30, and the powdercollection unit 40 from the three-dimensional formation apparatus 100 ofthe first embodiment. Even in the three-dimensional formation apparatus100 a, it is possible to form a three-dimensional object by performingthe same process as that of the three-dimensional formation apparatus100 of the first embodiment, except for the process of forming thepowder layer. Even in the fifth embodiment, it is possible to form athree-dimensional object using the support material, in the same manneras in the second embodiment. When the support material is used in thefifth embodiment and an area of a cross section on an upper layer islarger than an area of a cross section on a lower layer, it is possibleto support the portion having the larger area with the support materialon the lower layer.

F. Modification Examples First Modification Example

In the embodiments, the timing for performing the temporary curing andthe final curing by the curing energy application units 60 is notlimited to the timing shown in FIG. 8, and can be appropriately setaccording to chemical properties of the curable liquid (or the supportmaterial, same applied to the followings) or scattering speed of thecurable liquid. For example, the temporary curing may be executed fromthe execution of the cross section object formation process and untilthe filling process is started. In addition, the final curing may beexecuted at any timing from the execution of the filling process anduntil the next cross section object formation process is executed. Thefinal curing may be performed after sufficient time has elapsed untilthe difference-in-level portion is filled with the curable liquiddischarged to the thinner portion by the filling process.

Second Modification Example

In the embodiments, the temporary curing and the final curing areperformed after discharging the curable liquid, but any one of thetemporary curing and the final curing can be omitted. Both of thetemporary curing and the final curing may be omitted depending on thematerial of the curable liquid or the powder. As an example in whichboth curing processes are not performed, an adhesive (binder) may beused as the curable liquid and gypsum powder may be used as the powder.The kind of the curing energy is also not limited to the ultravioletlight and can be appropriately changed depending on the properties ofthe curable liquid or the powder.

Third Modification Example

In the embodiments, the head unit 50 moves relatively in the Z directionby moving the formation stage 11 in the Z direction. Meanwhile, theposition of the formation stage 11 may be fixed and the head unit 50 maybe directly moved in the Z direction. In addition, in the embodiments,the head unit 50 moves in the X direction and the Y direction, but theposition of the head unit 50 moves in the X direction and the Ydirection may be fixed and the formation stage 11 may move in the Xdirection and the Y direction.

Fourth Modification Example

In the embodiments, among the three-dimensional formation processesshown in FIG. 2, the acquisition of the three-dimensional data in StepS100, the smoothing process in Step S200, and the generation of the maindata and the auxiliary data in Step S300 are executed by the computer200. Meanwhile, the steps may be executed by the three-dimensionalformation apparatus 100. That is, the three-dimensional formationapparatus 100 may singly execute all processes from the acquisition ofthe three-dimensional data to the formation of the three-dimensionalobject. In the embodiments, Steps S400 to S900 of the three-dimensionalformation process shown in FIG. 2 are executed by the control unit 70 ofthe three-dimensional formation apparatus 100. Meanwhile, the steps maybe executed by controlling each unit of the three-dimensional formationapparatus 100 by the computer 200. That is, the computer 200 may realizethe function of the control unit 70 of the three-dimensional formationapparatus 100.

Fifth Modification Example

In the embodiments, the head unit 50 discharges the curable liquid inthe vertical direction, but may discharge the curable liquid in thehorizontal direction or the other directions and form thethree-dimensional object.

Sixth Modification Example

In the embodiments, when the curable liquid containing the quantitycorresponding to the gradation value is discharged to the head unit 50,the control unit 70 selects the quantity closest to the designatedgradation value among the predetermined kinds of quantity. Meanwhile,the control unit 70 can form the dots with the more kinds of thequantity of the curable liquid, by discharging the curable liquidcontaining the single quantity or the curable liquid containing fewerkinds of quantity to the same position several times.

The invention is not limited to the embodiments or the modificationexamples described above and can be realized with various configurationswithin a range not departing from a gist thereof. For example, theembodiments corresponding to the technical features in each aspectdisclosed in the summary or the technical features in the modificationexamples can be appropriately replaced or combined with each other, inorder to solve a part or all of the problems described above or toachieve a part or all of the effects described above. If the technicalfeatures are not described as compulsory in this specification, thosecan be appropriately deleted.

The entire disclosure of Japanese Patent Application No. 2014-065415,filed Mar. 27, 2014 and No. 2014-249659, filed Dec. 10, 2014 areexpressly by reference herein.

What is claimed is:
 1. A three-dimensional formation apparatus whichforms a three-dimensional object, the apparatus comprising: a head unitwhich discharges liquid which is one material of the object in a firstdirection, among the first direction, a second direction, and a thirddirection orthogonal to each other; and a control unit which forms theobject by laminating a plurality of cross section objects by executing across section object formation process of forming a cross section objectfor one layer of the object several times by discharging a quantity ofthe liquid equal to or smaller than a first quantity to a designatedcoordinate among coordinates representing a position in the seconddirection and a position in the third direction, by controlling the headunit, wherein the control unit forms a hollow on a changed portion wherean outline of the cross section object is simultaneously changed in thesecond direction and the third direction towards the inside from theoutline of the cross section object in the second direction or the thirddirection, in the first cross section object formation process among thecross section object formation processes executed several times, andexecutes a filling process of discharging a second quantity of theliquid which is larger than the first quantity to the hollow so as tocome in contact with the cross section object formed in the first crosssection object formation process, to fill at least a part of the hollowwith the liquid, after the first cross section object formation processis executed and before the second cross section object formation processis executed.
 2. The three-dimensional formation apparatus according toclaim 1, further comprising: a curing energy application unit whichapplies curing energy for curing the liquid, wherein the curing energyapplication unit applies the curing energy to the discharged liquid,after the liquid is discharged in the first cross section objectformation process and before the filling process is executed at aninterval of a first time period, and applies the curing energy to thedischarged liquid, after the liquid is discharged in the filling processand before the second cross section object formation process is executedat an interval of a second time period which is longer than the firsttime period.
 3. The three-dimensional formation apparatus according toclaim 1, wherein the coordinate to which the liquid is discharged in thecross section object formation process has each element corresponding toeach coordinate and is designated by two-dimensional raster data inwhich a gradation value corresponds to the each element, and the changedportion is a portion including a first element in which the gradationvalue is less than 100% and a second element which comes in contact withthe inside of the first element on the second direction side or thethird direction side, when a portion corresponding to the outline of thecross section object of the raster data is subjected to a smoothingprocess.
 4. The three-dimensional formation apparatus according to claim3, wherein the second quantity is a quantity corresponding to a valueobtained by adding the gradation value of the first element and thegradation value of the second element.
 5. The three-dimensionalformation apparatus according to claim 3, wherein the shape of theobject is represented with polygon data which is an assembly of aplurality of polygons, and the first element is an element correspondingto a position where the polygon crosses.
 6. The three-dimensionalformation apparatus according to claim 5, wherein the gradation value ofthe first element is a value corresponding to a ratio of a volumeremaining when a volume is cut by the polygon, to the volume of thefirst element occupying a three-dimensional space.
 7. Thethree-dimensional formation apparatus according to claim 5, wherein thesecond element is an element adjacent to a direction of a largecomponent among a component in the second direction and a component inthe third direction of an inward normal line of the polygon whichcrosses the first element, among an element in the second directionadjacent to the first element and an element in the third directionadjacent to the first element.